We report the results of a pilot survey for X-ray emission from a newly discovered class of AGB stars with far-ultraviolet excesses ( fuvAGB stars ) using XMM-Newton and Chandra . We detected X-ray emission in 3 of 6 fuvAGB stars observed – the X-ray fluxes are found to vary in a stochastic or quasi-periodic manner on roughly hour-long times-scales , and simultaneous UV observations using the Optical Monitor on XMM for these sources show similar variations in the UV flux . These data , together with previous studies , show that X-ray emission is found only in fuvAGB stars . From modeling the spectra , we find that the observed X-ray luminosities are \sim ( 0.002 - 0.2 ) L _ { \odot } , and the X-ray emitting plasma temperatures are \sim ( 35 - 160 ) \times 10 ^ { 6 } K. The high X-ray temperatures argue against the emission arising in stellar coronae , or directly in an accretion shock , unless it occurs on a WD companion . However , none of the detected objects is a known WD-symbiotic star , suggesting that if WD companions are present , they are relatively cool ( < 20 , 000 K ) . In addition , the high X-ray luminosities specifically argue against emission originating in the coronae of main-sequence companions . We discuss several models for the X-ray emission and its variability and find that the most likely scenario for the origin of the X-ray ( and FUV ) emission involves accretion activity around a companion star , with confinement by strong magnetic fields associated with the companion and/or an accretion disk around it .